In this talk, the problem of robust stabilization of bilinear control systems is considered. Based on the technique of linear matrix inequalities and quadratic Lyapunov function, the so-called robust stabilizability ellipsoid is designed such that the trajectory of the closed-loop system, starting inside the ellipsoid asymptotically tends to zero for all admissible uncertainties. The results obtained allow to design an approximation of the robust stabilizability domain of the uncertain bilinear control system.